Utilizing a Global Network of Telescopes to Update the Ephemeris for the Highly Eccentric Planet HD 80606 b and to Ensure the Efficient Scheduling of JWST

The transiting planet HD 80606 b undergoes a 1000 fold increase in insolation during its 111 days orbit due to it being highly eccentric (e = 0.93). The planet's effective temperature increases from 400 to over 1400 K in a few hours as it makes a rapid passage to within 0.03 au of its host star during periapsis. Spectroscopic observations during the eclipse (which is conveniently oriented a few hours before periapsis) of HD 80606 b with the James Webb Space Telescope (JWST) are poised to exploit this highly variable environment to study a wide variety of atmospheric properties, including composition, chemical and dynamical timescales, and large scale atmospheric motions. Critical to planning and interpreting these observations is an accurate knowledge of the planet's orbit. We report on observations of two full-transit events: 2020 February 7 as observed by the TESS spacecraft and 2021 December 7-8 as observed with a worldwide network of small telescopes. We also report new radial velocity observations which, when analyzed with a coupled model to the transits, greatly improves the planet's orbital ephemeris. Our new orbit solution reduces the uncertainty in the transit and eclipse timing of the JWST era from tens of minutes to a few minutes. When combined with the planned JWST observations, this new precision may be adequate to look for non-Keplerian effects in the orbit of HD 80606 b.